The Labor Party has condemned the Federal Government's silence on the details of the rift with Indonesia over border protection.

Indonesia has frozen people smuggling cooperation measures after leaked documents revealed Australian agencies spied on the president, his wife and inner circle in 2009.

During his weekly briefing today on asylum seeker arrivals, Immigration Minister Scott Morrison said he was sure Indonesia would continue with strong border protection measures because it's in Jakarta's "national interest".

He maintained Australia's efforts to stop the boats will go forward "unaffected".

But when he was pressed for more detail about how the diplomatic impasse will affect border protection operations, Mr Morrison said commenting further on "sensitive" issues would "not assist" the national interest.

Prime Minister Tony Abbott has taken the lead on dealing with the issue and his office has told the ABC a running commentary will not be provided.